Cosmological constant roll of inflation within Finsler-barthel-Kropina geometry: A geometric approach to early universe dynamics

This present work delves into the study of cosmological constant roll inflation, approaching it through the lens of Finsler-Barthel-Kropina geometry. This novel framework explains the conventional understanding of the large-scale structure of universe's homogeneity and isotropy with small-scale presence of anisotropy. The methodology employed in this work involves translating the concept of osculating Riemannian space into the context of Finsler spaces. By harnessing the unique metric structure of Kropina space, the primary focus is on unravelling the intricacies of the inflationary phenomenon. The study reveals that by introducing the anisotropic parameter $\eta$ into the metric structure and Hubble parameter, a comprehensive explanation for the anisotropic expansion of the universe can be achieved. Through a careful analysis of slow roll parameters, the research delves into the dynamics of inflation on a macroscopic scale, shedding light on the influence of anisotropy on both scalar and tensor perturbations within the power spectrum. Ultimately, the core aim of this study is to establish that the Finslerian analogy of inflation finds a coherent explanation within the framework of Kropina geometry.